Universal increment

Conformational shift effects could be discussed in terms of discrete rotational isomeric states. Mainly two effects could be derived empirically to explain the shift differences due to conformational isomerism they-gauche and the Vg effect. However the spectra also indicate that the y-gauche effect is not a quantity with a universal numerical value. Furthermore the spectra of the cycloalkanes show that the conformational effects do not obey simple rules of additivity. With concern to our present knowledge great care has to be taken for the interpretation of NMR-spectra on the base of conformational shift increments which were not determined for the specific molecular structures. 

Theisen C, Johann C, Deacon MP, Harding SE (2000) Refractive Increment Data Book for Polymer and Biomolecnlar Scientists. Nottingham University Press, Nottingham, UK... 

The viscosity increment Ua-b is referred to as a universal shape fimction or Simha number (table 4) it can be directly related to the shape of a particle independent of volume. For its experimental measurement it does however require measurement of Usp, v, 5, po, as well as of course [rj]. 

We take here twice the universal methylene increment (cf Reference 1) as found in the liquid state, i.e. 20.6 + 4.7 where 20.6 is the usually proposed (gas phase) value and 4.7 is (within a sign) the enthalpy of vaporization or condensation per carbon for an arbittary organic compound as suggested in Reference 4. 

While there is some dispute about how universal the universal methylene increment really is (cf Reference 1), it is nonetheless generally conceded that a methylene group affixed to two carbons usually contributes ca — 21 kJ mol-1 to the gas phase enthalpy of formation. 

Boyes, Gai and coworkers at the University of Oxford (in association with JEOL Ltd) (33) and by Thomas and coworkers at the University of Cambridge (also in association with JEOL Ltd) (34,35). The key points of these developments were that the instrument had a resolution similar to that of the best home-built HRTEM instruments ( 2 A) at a small fraction of the cost, and it came in a user-friendly package, achieving the full theoretical performance routinely while fitting in a standard laboratory and requiring no special buildings. Incremental improvements in resolution (—1.3-1.6 A) were achieved later with the development of a 400-kV HRTEM (36). 

The slopes, ag, for various n-alkyl substituted homologous series are commonly compared to the universal slope (methylene increment) of —20.6 kJmol-1 calculated for the n-alkanes9. An unanswered question is whether for Targe enough nc the methylene increment should be identical for all functionalized alkanes. In previous studies it is shown that the slopes vary, although not too widely (ca 2 kJ mol-1), and there is no discernible relationship between the functional group and a. With three exceptions, the slopes reported in Table 1 are in line with those calculated for other functional group series. 

To use what is termed universal kriging, it is assumed that Z(2 ) is an intrinsic random function of order k. But the problem of identifying the drift and the semi-variogram when they are both unknown is still present. However, Matheron (11) defined a family of functions called the generalized covariance, K(h). and the variance of the generalized increment of order k can be defined in terms of K(h ). That is. 

If there were ever a simple comparison of enthalpies of formation to be investigated as part of this chapter it would be the oximes of the aliphatic aldoximes, RCH=NOH, as R proceeds through Me, Et, n-Pr,. Ideally, we would have the values for at least R = Me and Et and then employ the universal methylene increment to derive the remaining values by addition of —20.6 kJmoR for gaseous species and a related ca —26.0 kJ moR for... 

G. Geiseler, M. Ratzsch, K. Ebster and E. Ziegel, Ber. Bunsenges. Phys. Chem., 70, 221 (1966). J. D. Cox and G. Pilcher, Thermochemistry of Organic and Organometallic Compounds, Academic Press, London, 1970. In addition, the universal methylene increment has been a major tool in our analyses of literature thermochemical data in many of our earlier Patai/Rappoport chapters, e.g. References 8 and 9. 

Price discrimination refers to the practice of selling identical products to different sets of customers at different prices. Expressed another way, different customers pay different markups over the identical incremental cost of producing an identical product. Price discrimination is widely practiced in the hotel and airline industries, by universities in the United States that can vary their tuition through scholarships, by electric power companies, and in the health care industry. Hospitals in the United States, for example, routinely charge different payers different prices for the same services. In the U.S. pharmaceutical market, different prices are charged to different insurance carriers and to self-paying patients. Worldwide, the same pharmaceutical firms sell the identical product to different countries at different prices. 

The linear correlation of enthalpies of formation with the number of carbon atoms is a useful and well-known feature of homologous series of functionalized organic compounds. The slope of the regression line for the gaseous n-alkanes (CH3—(CH2)j —H), —20.6 kJmol-, and the similar values of the slopes for other CH3—(CHi) —Z series is often called the universal methylene increment . In the liquid phase, the increment for the n-alkanes is —25.6 0.1 klmoD. The most accurate determination of the increment... 

In obtaining Equation 11 it has been assumed that the partial specific volumes v of the associating species are equal we have also assumed that the specific refractive index increments of the associating solutes are equal. In Equation 12 R is the universal gas constant (8.314 X 107 ergs/deg-mole), p is the density of the solution (gram/ml), and T is the absolute temperature. Equation 11 is also valid for the Archibald experiment but only at rm or rb, the radial positions (in the solution column of the ultracentrifuge cell) of the air-solution meniscus and of the cell... 

Insertion of a methylene group into a molecule causes a decrease in aqueous solubility, however not with a universally applicable constant increment, as available GCMs might suggests. The odd-even effect (see Section 11.3) and the chain length have to be considered for accurate, quantitative estimations. In addition polar groups in the molecule affect the methylene contribution, as the following rule illustrates ... 

Systematic spacing of increments collected from a stopped belt is accepted universally as the reference method of sampling that is intrinsically bias-free. Stationary sampling, that is, sampling coal at rest in piles, or in transit in trucks, railcars, barges, and ships, suffers decreased reliability to an indeterminate degree. 

There is no question from what we have heard that university research is of increasing importance to industry and that this is controversial. Big companies have been neglecting basic research. For example, the number of publications from IBM and Bell Laboratories dropped by a factor of 2 between 1985 and 1995. At this rate it is clear that universities will be of increasing importance to industrial research. Within the industrial portfolio, there are high-risk/high-reward investments and there are low-risk/incremental improvement investments. Universities can, in principle, be leveraged for benefits in both scenarios, but in reality universities are much better suited to the former. 

A price of our analysis is that the enthalpy of formation of some of the CH3XYZCH3 species will have to be estimated. In principle, one could use Benson group increments [28] in lieu of these estimates but then, many of these increments would also have to be estimated because many compounds containing the groups are unknown, inadequately precedented, or even limited to but one species, the one of interest. Benson said in a related context to one of the authors (JFL) some decades ago If the universe was kind, your approach would agree with mine, and both would agree with the universe. ... 

---